Successive coefficients for spirallike and related functions

We consider the family of all analytic and univalent functions in the unit disk of the form $f(z)=z+a_2{z}^2+a_3{z}^3+\cdots$. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is $\mid \mathrm{\mid }{a}_{n+1}\mathrm{\mid }-\mathrm{\mid }{a}_n\mathrm{\mid }\mid$, for $f$ belonging to the family of $\gamma$-spirallike functions of order $\alpha$. Our particular results include the case of starlike and convex functions of order $\alpha$ and other related class of functions.